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Structural and computational understanding of tensors is the driving forcebehind faster matrix multiplication algorithms, the unraveling of quantumentanglement, and the breakthrough on the cap set problem. Strassen'sasymptotic spectra program (FOCS 1986) characterizes optimal matrixmultiplication algorithms through monotone functionals. Our work advances andmakes novel connections among two recent developments in the study of tensors,namely  - the slice rank of tensors, a notion of rank for tensors that emerged fromthe resolution of the cap set problem (Ann. of Math. 2017),  - and the quantum functionals of tensors (STOC 2018), monotone functionalsdefined as optimizations over moment polytopes.  More precisely, we introduce an extension of slice rank that we call weightedslice rank and we develop a minimax correspondence between the asymptoticweighted slice rank and the quantum functionals. Weighted slice rankencapsulates different notions of bipartiteness of quantum entanglement.  The correspondence allows us to give a rank-type characterization of thequantum functionals. Moreover, whereas the original definition of the quantumfunctionals only works over the complex numbers, this new characterization canbe extended to all fields. Thereby, in addition to gaining deeper understandingof Strassen's theory for the complex numbers, we obtain a proposal for quantumfunctionals over other fields. The finite field case is crucial forcombinatorial and algorithmic problems where the field can be optimized over.

Weighted slice rank and a minimax correspondence to Strassen's spectra